THE VIBRATIONAL RESPONSE OF A CLAMPED RECTANGULAR POROUS PLATE

The vibrations of a rectangular porous plate can be described by two coupled equations involving the time and space derivatives of the deflection and of the relative fluid–solid motion. These equations were established previously and are solved in the present article by Galerkinʹs variational method. As in the classical theory of plates (non-porous), the solutions are approximate and their mathematical form is chosen. The Rayleigh–Ritz decomposition on the basis of orthogonal or quasi-orthogonal eigenfunctions is used and the solutions are inserted in the vibrational equations. This procedure leads to an explicit form for the solid lateral deflection wsand for the fluid–solid relative diplacement w within the pores. In this study, the chosen eigenfunctions or trial functions are obtained from the linear combination of sinusoidal and hyperbolic functions. The solutions have a single generic form allowing one to account for any boundary condition at the edges involving simply supported, free or clamped edges. Numerical results are given for three different porous plates with the four edges clamped. Simple experiments have also been carried out in order to check the validity of the method. The results are presented and compared with the predictions.